If y varies inversely as x squaredand y = 6 when x = 30, what is y when x = 6?

Call a bottle of juice costs is x

$2.49 + 12x = $27.57

             12x = $27.57 - $2.49

             12x = $25.08

                 x = $25.08 / 12

                 x = $2.09

SO each bottle of juice costs $2.09.

Mark as Brainliest If the answer is helpful!

Answer:

15.3 L

Step-by-step explanation:

1% of 15 is 15÷100=0.15

0.15×2=0.3, so 2% is 0.3

15+0.3=15.3

Answer:

(x + 5) (x^2 -3)

Step-by-step explanation:

[tex]x^{3} +5x^{2} - 3x - 15[/tex]

Do the grouping:

[tex]x^{3} +5x^{2} - 3x - 15 = (x^{3} +5x^{2}) + (-3x - 15)[/tex]

Then factor out [tex]x^{2}[/tex] in the first and −3 in the second group.

[tex]x^{2}(x+5) - 3(x+5)[/tex]

Factor out the common term x + 5 by using the distributive property.

Polynomial [tex]x^{2}-3[/tex] is not factored in since it does not have any rational roots, thus getting the following:

[tex](x+5)(x^{2} -3)[/tex]

Answer:

the fourth option (x+5)(x²-3)

Step-by-step explanation:

the "-15" tells us we need a 3 and a 5 with different signs.

that eliminates the first and the second options.

and the "5x²" tells us it has to be +5, as there is only one part in the whole multiplication that delivers a x² term (5×x²).

it is also confirmed for the same reasons by "-3x" that the other number has to be -3.

cos(4x + π/5) - sin(2x) = 0

Since cos(x + π/2) = -sin(x), we can write

cos(4x + π/5) = cos(4x + π/2 - 3π/10) = -sin(4x - 3π/10)

Then we can absorb the negative signs into either sin expression, using the fact that sin(-x) = -sin(x):

-sin(4x - 3π/10) - sin(2x) = 0

sin(3π/10 - 4x) + sin(-2x) = 0

Recall that

• sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

• sin(a - b) = sin(a) cos(b) - cos(a) sin(b)

==>   • 2 sin(a) cos(b) = sin(a + b) + sin(a - b)

We can further condense the left side in our equation if there exists a solution to

{ 3π/10 - 4x = a + b

{ -2x = a - b

We have

(a + b) + (a - b) = (3π/10 - 4x) + (-2x)

==>   2a = 3π/10 - 6x

==>   a = 3π/20 - 3x

(a + b) - (a - b) = (3π/10 - 4x) - (-2x)

==>   2b = 3π/10 - 2x

==>   b = 3π/20 - x

So in our equation, we have

sin(3π/10 - 4x) + sin(-2x) = 0

2 sin(3π/20 - 3x) cos(3π/20 - x) = 0

sin(3π/20 - 3x) cos(3π/20 - x) = 0

Solve for x :

sin(3π/20 - 3x) = 0   or   cos(3π/20 - x) = 0

[3π/20 - 3x = arcsin(0) + nπ   or   3π/20 - 3x = π - arcsin(0) + nπ]

  or   [3π/20 - x = arccos(0) + nπ   or   3π/20 - x = -arccos(0) + nπ]

[3π/20 - 3x = nπ   or   3π/20 - 3x = π + nπ]

  or   [3π/20 - x = π/2 + nπ   or   3π/20 - x = -π/2 + nπ]

[3x = 3π/20 - nπ   or   3x = -17π/20 - nπ]

  or   [x = -7π/20 - nπ   or   x = 13π/20 - nπ]

[x = π/20 - nπ/3   or   x = -17π/60 - nπ/3]

  or   [x = -7π/20 - nπ   or   x = 13π/20 - nπ]

(where n is any integer)

Answer:

4

Step-by-step explanation:

Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have

population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as

(original population)*1.011ˣ

Therefore, to get from 7 billion to 7.31 billion, we have

7 billion * 1.011ˣ = 7.31 billion

divide both sides by 7 billion to relatively isolate the x

1.011ˣ = 7.31/7

Another way of writing this is

log (base 1.011) (7.31/7) = x

≈ 3.96

Rounding to the nearest whole number, we get 4 as our answer

The number of years it takes for the population to grow from 7 billion to 7.31 billion is;

n = 4 years.

We are told that the population of the world grows exponentially by 1.1% per year. This is equivalent to growth of 0.011 per year exponentially.

Now, since the exponential rate is 0.011 per year, thus, if the original population is P, then after a year, the new population will be;

P_1 = 1.011¹ × P

After 2 years, it will be;

P_2 = 1.011² × P

Thus, if n represents the number of years after the initial population, then population after n years if original population is P is;

P_n = 1.011ⁿ × P

Now, we are told that the population grew from 7 billion to 7.31 billion.

Thus;

P = 7 billion

P = 7 billion P_n = 7.31 billion

Thus;

7 billion × 1.011ⁿ = 7.31 billion

divide both sides by 7 billion to get;

1.011ⁿ = 7.31/7

1.011ⁿ = 1.044285

n log 1.011 = log 1.044285

n = 0.018819/0.004751156

n ≈ 4 years

Read more at; https://brainly.in/question/21384543

Answer:

G. 105.

Step-by-step explanation:

Percentage of cars with  3 or more people

= 15 + 7 + 3

= 25%,

25% of 420

= 0.25 * 420

= 105.

Answer:

There are no solutions.

The left side of the equation will always be three less than the right side of the equation since both sides have the same variable.

Hi! I'm happy to help!

For this, you just simply follow the directions, and alter as you go. First, we need to place E between F and G, so we can put F and G on opposite sides of E.

F   E   G

From here, we put H between F and E

F   H   E   G

I hope this was helpful, keep learning! :D

Answer:

mean=71

Step-by-step explanation:

Mean x¯¯¯x¯

71

Median x˜x~

72

Mode

64, 83, 79, 38, 81, 90, 59, 93, 70, 73, 71, 51

Range

55

Minimum

38

Maximum

93

Count n

12

Sum

852

Quartiles

Quartiles:

Q1 --> 61.5

Q2 --> 72

Q3 --> 82

Interquartile

Range IQR

20.5

Outliers

none

Answer:

Max drove half an hour at 110 miles per hour.

Step-by-step explanation:

185 = 65(2) + 110t

185 = 130 + 110t

-130    -130

---------------------------

55 = 110t

/110    /110

----------------------------

0.5 = t

Answer:

Distance cannot be negative because no matter which direction you travel, you will never travel negative units.

Step-by-step explanation:

Distance cannot be negative in the same way that when you put a car in reverse, the odometer does not go backwards.

If you have a mailbox 30 feet east of your house and a park 30 feet west of your house, you can think of it like a number line: your house is 0, the park is -30 and the mailbox is 30. But, if you walk to your park, you have not walked -30 feet.

Answer:

12. This is because of the commutative property of addition.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Using the commutative property of addition

8+4 = 12

4+8 = 12

Answer:

1: 5 2: 13 3: sqr root of 15 4: 1 5: 1 6: 3

Step-by-step explanation:

Follow the formula a squared plus b squared equals c squared. C is always the longest side of the equation. So figure out your variables to fill in and in the end, square root your remaining answer.

The values of the angles are;

x = 12°

m∠PQS = 71°

m∠PQT = 142°

m∠TQR = 41°

The reason the above values are correct is as follows:

Question: The part of the question that appears missing as obtained online is as follows;

The required angles: x, m∠PQS, m∠PQT, and m∠TQR

Please see attached drawing of the angles from the question

The given parameters are;

[tex]\overset{\longrightarrow}{QS}[/tex] bisects ∠PQT

m∠SQT = (8·x - 25)°

m∠PQT = (9·x + 34)°

m∠SQR = 112°

We have;

m∠PQT = m∠SQT + m∠PQS (Angle addition postulate)

m∠SQT ≅ m∠PQS (Angles formed by angle bisector are congruent)

m∠SQT = m∠PQS Definition of congruency

m∠PQT = 2 × m∠SQT

Therefore;

(9·x + 34)° = 2 × (8·x - 25)° = (16·x - 50)°

Collecting like terms gives;

(34 + 50)° = 16·x - 9·x = 7·x

7·x = 84°

x = 84°/7 = 12°

x = 12°

m∠SQT = (8·x - 25)°

Therefore;

m∠SQT = (8 × 12 - 25)° = 71°

m∠SQT = 71°

m∠PQT = 2 × m∠SQT

∴ m∠PQT = 2 × 71° = 142°

m∠PQT = 142°

m∠PQS = m∠SQT (Angles formed by the same bisector [tex]\overset{\longrightarrow}{QS}[/tex])

∴ m∠PQS = m∠SQT = 71°

m∠PQS = 71°

m∠SQR = m∠SQT + m∠TQR (Angle addition postulate)

m∠SQT = 71°

∴  m∠SQR = 112° = 71° + m∠TQR

m∠TQR = 112° - 71° = 41°

m∠TQR = 41°

Learn more about finding angles with algebraic expressions here:

https://brainly.com/question/21607755

Answer:

(4,3)

Step-by-step explanation:

If the triangle ABC is moved 5 units to the right, the coordinates of A will be (4,3). We can find this by using the values already given for A. We are given (-1,3) which is A's current position. Since we are moving it to the right we are only looking at the first number. If we add 5 to -1 we get 4 which we put in the place of the -1 in the coordinates to get our answer.

Answer:

B. x = 31; m∠ROS = 62°

Step-by-step explanation:

Complementary angles add to 90

∠ROQ + ∠ROS = 90

28+2x = 90

Subtract 28 from each side

2x = 90-28

2x=62

Divide by 2

2x/2 = 62/2

x = 31

∠ROQ =28

∠ROS = 2x=2*31 = 62

Answer:

give brainliest please I need it to level up

Step-by-step explanation:

16 - 2t + 5t + 9

16 + 9 -2t + 5t=0

25 + 3t =0

3t= -25

t= -8.3

Answer:

thanks for points

Step-by-step explanation:

too easy boi

Answer:

A

Step-by-step explanation:

p^-8q^-20 * p^8q^-10

=q^-30

=1/q^30

Answer:

84.861

Step-by-step explanation:

In the given figure, 1/4 part of Circle is missing

so, we have to find the area of 3/4 part of circle

Area of circle = πr²

Given, r = 6

Now, Area of 3/4 part of circle = (3/4)×πr²

= (3/4) × 3.143 × 6²

= 84.861

Step-by-step explanation:

X = Acceleration × time

=300× (10/60)

=50km/h

Answer:

[tex]7 \times 6 = 5 \: sixes + 2 \: sixes \\ 7 \times 6 = 30 + 12 \\ = 42 \\ \\ thank \: you[/tex]

Hi ;-)

[tex]7\cdot6=5 \ \text{sixes}+\boxed2 \ \text{sixes}\\\\=\boxed{30}+12\\\\=\boxed{42}[/tex]

By looking at the dot graph, we can see that the single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was 12 mg/L

To understand this, first I want to give a brief explanation of how these graphs work.

You know that the ecologist did study the Nitrate pollution at 42 places in two lakes.

Each of these 42 places is represented with a dot in the corresponding graph.  Now looking at the graph, the position of the dots represents the nitrate concentration (you can see it in the horizontal axis) on one of these 42 places (42 dots for 42 places).

So, having a single dot above 12 in the Stony Brook graph, means that the ecologist find that in one of the 42 places measured in the Stony Brooks lake, the nitrate concentration was of 12 mg/L

If you want to learn more, you can read:

https://brainly.com/question/16354226

Step-by-step explanation:

Elisa made the greater number of withdrawals, because she made 9 withdrawals, while Frances only made 6 withdraws.

Answer:

x = 3+y/2

Step-by-step explanation:

Answer:

31.1011905%

Step-by-step explanation:

Take the new price and subtract the original price

8.81 - 6.72

2.09

Divide by the original price

2.09/6.72

.311011905

Change to percent form

31.1011905%

Percent of increase in average movie theatre ticket price will be 31.1%

    Given prices of the ticket in two different years are,

To calculate the percent increase in the price of an object expression to be used,

Percent increase = [tex]\frac{\text{Final price - Initial price}}{\text{Initial price}}\times 100[/tex]

                             = [tex]\frac{8.81-6.72}{6.72}\times 100[/tex]

                             = [tex]0.311\times 100[/tex]

                             = [tex]31.10[/tex]%

          Therefore, percent of increase in the price of the ticket will be 31.1%

Learn more,

https://brainly.com/question/11265758